$C_3$-equivariant stable stems
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914487196450816 |
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| author | Hou, Yueshi Zhang, Shangjie |
| author_facet | Hou, Yueshi Zhang, Shangjie |
| contents | We compute the spoke-graded $C_3$-equivariant stable homotopy groups of spheres $π_{i, j}^{C_3}$, for stems less than 25 (i.e. $i\leq 25$) and for weights between -16 and 16 (i.e. $-16\leq j\leq 16$). In particular, for $j=2k$, this corresponds to the usual $RO(C_3)$-graded homotopy groups of spheres $π^{C_3}_{i-j+kλ}$ for some fixed 2-dimensional $C_3$-faithful representation $λ$. We also describe the geometric fixed point map $Φ^{C_3}: π_{i, j}^{C_3}\to π_{i-j}^{cl}$ and the underlying map $Res: π_{i, j}^{C_3}\to π_{i}^{cl}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C_3$-equivariant stable stems Hou, Yueshi Zhang, Shangjie Algebraic Topology We compute the spoke-graded $C_3$-equivariant stable homotopy groups of spheres $π_{i, j}^{C_3}$, for stems less than 25 (i.e. $i\leq 25$) and for weights between -16 and 16 (i.e. $-16\leq j\leq 16$). In particular, for $j=2k$, this corresponds to the usual $RO(C_3)$-graded homotopy groups of spheres $π^{C_3}_{i-j+kλ}$ for some fixed 2-dimensional $C_3$-faithful representation $λ$. We also describe the geometric fixed point map $Φ^{C_3}: π_{i, j}^{C_3}\to π_{i-j}^{cl}$ and the underlying map $Res: π_{i, j}^{C_3}\to π_{i}^{cl}$. |
| title | $C_3$-equivariant stable stems |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2505.10745 |